Hydrodynamic interaction between particles near elastic interfaces

TL;DR

This paper provides an analytical framework for understanding hydrodynamic interactions between particles near elastic interfaces, revealing unique behaviors such as attraction or repulsion depending on membrane properties and frequency, with validation from simulations.

Contribution

The study introduces a detailed analytical model for particle interactions near elastic membranes, incorporating finite size effects and frequency dependence, and compares results with boundary integral simulations.

Findings

Particles near membranes with bending resistance are mutually repelled.

Membranes with shearing resistance can induce attractive interactions.

Frequency-dependent effects can lead to superdiffusive particle motion.

Abstract

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.